Transient study of a discrete-time queueing model with feedback mechanism

摘要

A discrete-type queueing model with finite buffer capacity is studied. The input flow of incoming jobs is modelled by interarrival times with a common geometric distribution, while processing times are supposed to be generally distributed and the service process is organized according to the FIFO discipline. A feedback mechanism is implemented in that each job after its processing can be returned back to the accumulating buffer with the so-called feedback probability f ∈ [0, 1). In such a case a returning job is positioned at the end of the queue and waits for the processing once more. The number of potential feedbacks is unbounded. The time-dependent queue behavior is investigated and the compact-form representation for the probability generating function of the queue-size distribution is obtained. The considered queueing system can be used in modelling of the telecommunication traffic in that discrete times (time slots) are usually considered. The feedback mechanism can be applied as a model of retransmission, e.g. due to bit errors, where f can be then treated as a percentage of packets which must be retransmitted at least one time.